According to Niels Bohr quantum theory must be interpreted, not as\na description of nature itself, but merely as a tool for making predictions about observations appearing under conditions described by\nclassical physics: Strictly speaking, the mathematical formalism of quantum theory\n... merely offers rules of calculation for the deduction of\nexpectations about observations obtained under well-defined\nconditions specified by classical physical concepts. 1 There can be no question of any unambiguous interpretation of\nthe symbols of quantum mechanics other than that embodied by\nthe well-known rules which allow to predict the results to be\nobtained by a given experimental arrangement described in a\ntotally classical way. 2 This necessity of discriminating in each experimental arrangement\nbetween those parts of the physical system considered which are\ntreated as measuring instruments and those which constitute the\nobject under investigation may indeed be said to form a principal\ndistinction bet»"een classical and quantum description ofphysical\nphenomena. 2 Indispensable use of classical concepts ... even though classical\nphysical theories do not suffice. 2 This indispensable use of the invalidated classical concepts is a\ntroublesome point. So is the intrusion into the theory of the scientist\nhimself; the scientist must make a somewhat arbitrary division of a\nsingle unified physical system into two separate parts, and describe\nthem according to mutually incompatible physical theories.
According to Niels Bohr quantum theory must be interpreted, not as\na description of nature itself, but merely as a tool for making predictions about observations appearing under conditions described by\nclassical physics: Strictly speaking, the mathematical formalism of quantum theory\n... merely offers rules of calculation for the deduction of\nexpectations about observations obtained under well-defined\nconditions specified by classical physical concepts. 1 There can be no question of any unambiguous interpretation of\nthe symbols of quantum mechanics other than that embodied by\nthe well-known rules which allow to predict the results to be\nobtained by a given experimental arrangement described in a\ntotally classical way. 2 This necessity of discriminating in each experimental arrangement\nbetween those parts of the physical system considered which are\ntreated as measuring instruments and those which constitute the\nobject under investigation may indeed be said to form a principal\ndistinction bet»"een classical and quantum description ofphysical\nphenomena. 2 Indispensable use of classical concepts ... even though classical\nphysical theories do not suffice. 2 This indispensable use of the invalidated classical concepts is a\ntroublesome point. So is the intrusion into the theory of the scientist\nhimself; the scientist must make a somewhat arbitrary division of a\nsingle unified physical system into two separate parts, and describe\nthem according to mutually incompatible physical theories.
What does not satisfy me in that theory [quantum mechanics], from the standpoint of principle, is its attitude towards that which appears to me to be the programmatic aim of all physics: the complete description of any (individual) real situation (as it supposedly exists irrespective of any act of observation or substantiation). Albert Einstein, Reply to Criticisms [This] implies the impossibility of any sharp separation between the behaviour of atomic objects and the interaction with the measuring instruments which serve to define the conditions under which the phenomena appear . In fact, the individuality of the typical quantum effects finds its proper expression in the circumstance that any attempt of subdividing the phenomena will demand a change in the experimental arrangement introducing new possibilities of interaction between objects and measuring instruments which in principle cannot be controlled. Consequently, evidence obtained under different experimental conditions cannot be comprehended within a single picture, but must be regarded as complementary in the sense that only the totality of the phenomena exhausts the possible information about the objects. Indeed the finite interaction between object and measuring agencies conditioned by the very existence of the quantum of action entails – because of the impossibility of controlling the reaction of the object on the measuring instruments, if these are to serve their purpose – the necessity of a final renunciation of the classical idea of causality and a radical revision of our attitude towards the problem of physical reality. […]
When investigating various interpretations of quantum mechanics one notices that each interpretation contains an element which escapes a complete and full description. This element is always associated with the stochasticity of the individual event in the quantum measurement process. It appears that the implications of this limit to any description of the world has not been sufficiently appreciated with notable exceptions of, for example, Heisenberg, Pauli and Wheeler. If we assume that a deeper foundation of quantum mechanics is possible, the question arises which features such a philosophical foundation might have. It is suggested that the objective randomness of the individual quantum event is a necessity of a description of the world in view of the significant influence the observer in quantum mechanics has. It is also suggested that the austerity of the Copenhagen interpretation should serve as a guiding principle in a search for deeper understanding. In recent years, a significant increase of interest in the foundations of quantum mechanics can be observed. This increase is certainly related to the immense progress made during the last two decades in experiments with individual quantum systems. This technological progress has made it possible to really perform more and more of the famous gedanken experiments which were so important in the early days of the theory. Not only did these experiments confirm the theory in every detail, they also opened up avenues for new experimental directions which might even lead some day to new technology. While such applications are certainly still far away, areas like quantum cryptography[1], quantum computation[2] and interaction-free measurement[3], just to name a few examples, certainly deserve the attention they receive. All this activity has also drawn more attention to the problems of understanding and interpreting quantum mechanics. It seems that there, a definitive consensus has not yet been reached. As witnesses quote authorities like Feynman as saying[4]: I think can safely say that nobody today understands quantum mechanics, whereby he apparently included himself, or like Roger Penrose[5], who describes his opinion remarking that while the theory agrees incredibly well with experiment and while it is of profound mathematical beauty, it makes absolutely no sense. Why did even physicists who have contributed so significantly to quantum theory Feynman was even rewarded the Nobel Prize for one of its mathematical formulations choose such emphatic and strong formulations? Why is it that the average physicist hears very little about such problems during his/her education? Why is the comprehension of the theory very often focused on formalism while questions that probe for deeper meaning are usually not tackled? To take a closer look at the situation, let us turn to a brief analysis of the interpretation of quantum mechanics. We note that there are at least two levels of interpreting a formalism, a physical theory. The first, basic, level supplies the rules that determine which element of the formalism corresponds to which measurable quantity or to which observable fact in a concrete experimental situation. Theses rules are a large, mostly not explicated but only implicit, set of instructions. These instructions concern the manner of working with the statements of the theory in order to obtain predictions for future experiments or events, and they concern the instructions on how to proceed in experiment in order to demonstrate or test a theoretical
Quantum theory is the soul of contemporary physics. It was discovered in an adventurous way, under the urge to solve the puzzles posed by atomic spectra and blackbody radiation. But after its invention, it immediately became clear that it was not just a theory of specific physical systems: it was rather a new language of universal applicability. Already in 1928, the theory had received solid mathematical foundations by Hilbert, von Neumann, and Nordheim, and this work was brought to completion in the monumental work of von Neumann, in the form that we still study nowadays. The theory is extraordinarily successful, and its predictions have been confirmed to an astonishing level of precision in a large spectrum of experiments. However, almost 90 years after von Neumann's book, quantum theory remains mysterious. Its mathematical formulation – based on Hilbert spaces and self-adjoint operators – is far from having an intuitive interpretation. The association of physical systems to Hilbert spaces whose unit vectors represent pure states, the representation of transformations by unitary operators and of observables by self-adjoint operators – all such postulates look artificial and ad hoc . A slightly more operational approach is provided by the C * -algebraic formulation of quantum theory – still, this formulation relies on the assumption that observables form an algebra , where the physical meanings of the multiplication and the sum are far from clear. In short, the postulates of quantum theory impose mathematical structures without providing any simple reason for this choice: the mathematics of Hilbert spaces is adopted as a magic blackbox that “works well” at producing experimental predictions. However, in a satisfactory axiomatization of a physical theory the mathematical structures should emerge as a consequence of postulates that have a direct physical interpretation. By this we mean postulates referring, e.g., to primitive notions like physical system, measurement, or process, rather than notions like, e.g., Hilbert space, C * -algebra, unit vector, or selfadjoint operator. The crucial question thus remains unanswered: why quantum theory? Which are the principles at the basis of the theory? A case that is often invoked in contrast is that of Special Relativity theory, which directly follows from the simple understandable principle of relativity.
Quantum theory is a mathematical formalism that allows physicists to predict the probability of observing different outcomes in experiments on sub-atomic systems. It has been tested more rigorously than any theory in science, and has never been wrong. However, strictly speaking it does not “explain” the behavior of sub-atomic systems, since it does not propose a mechanism to account for it. It tells us that they will behave in certain ways, but not why . Thus, quantum mechanics is not a theory in the sense familiar to social scientists, namely a body of laws that explains some part of reality. The explanatory question is the subject of the interpretive debates that surround the theory, not of the theory per se. That said, the literature routinely refers to quantum mechanics as a theory, and I shall use the terms interchangeably below. A common way to introduce quantum theory is through some of the key experiments that have confirmed its predictions. In this chapter I describe three of the most well-known: the Two-Slit Experiment, the Bell Experiments, and the Delayed-Choice Experiment. While painting the same overall picture, each reveals distinct features of the quantum realm. While their interpretation is contested, here I will do my best to present just the theory's findings, saving interpretive questions for later. The Two-Slit Experiment This experiment actually had its origins long before the quantum revolution. One of the most controversial questions in classical physics was whether light was made of particles or waves. In keeping with his atomistic worldview, Newton favored the particle or “corpuscular” theory of light, which was the majority view among physicists through the eighteenth century. However, in 1801 Thomas Young performed an experiment that seemed to prove conclusively that the wave theory was correct. In his experiment, Young set up a light source behind an opaque screen with one small opening or slit, through which the light passed in a concentrated beam.
Niels Bohr thought that what quantum mechanics has taught us is not only to understand something new, but also a new meaning of the term “to understand”. Bohr wanted to free himself from ontology by putting emphasis on epistemology; i.e. on certain conditions for observation and description. He believed that the epistemological lesson of quantum mechanics was a crucial one. Basically it has two important aspects. 1. Bohr's philosophy leads to a break with the so-called correspondence theory for truth and meaning. It states that true propositions are descriptions of a world that is independent of our observations; i.e. that on a regular basis one can compare with reality, that is, in compare the two areas against each other. Bohr believed that this did not make sense, since in many situations cannot add meaning to a world that has a sich structure (the thing-in-itself), which in turn can be depicted when observed. 2. All knowledge is attained under certain conditions for description. Bohr thought that the long-lasting criterion for valid knowledge is that can communicate it unambiguously to each other. When Bohr emphasised that we are suspended in language in the sense that all knowledge determines what can say about the world in an understandable way, and not what the world actually is, this must be understood in the sense that only know the world as recognised; i.e., structured on the basis of the conditions for description, to which are, as part of the world, necessarily are subjected to. Bohr's emphasis on conditions for descriptions invalidates the well-known distinction between analytic and synthetic propositions. An important feature of the descriptive use of ordinary language, as well as in classical physics, is that description is based on a dividing line between subject and object. This results in idealism and materialism not being tenable positions. Furthermore, it is such that cannot use the designation of things independently of the designation of time and space. Logical principles are only meaningfully applied in situations relating to our conditions for observation. So based on inspiration from Bohr, Favrholdt developed a more adequate and comprehensive philosophy, where he, among other things, states that all humans possess a fundamental language, underlying all languages. This constitutes a number of concepts – the core – where the correct use is dictated by the structure of the world, which humans learn through sensory perception and action.